Heat/mass transport in a drop translating in time-periodic electric fields

Enhancement of heat or mass transport in a spherical drop of a dielectric fluid translating in another dielectric fluid in the presence of uniform and non-uniform time periodic electric fields is investigated. The internal problem or the limit of the majority of the transport resistance being in the dispersed phase is considered. The transient energy conservation equation is solved using a fully implicit finite volume method. Lagrangian tracking of fluid particles is carried out to understand the extent of fluid mixing and heat/mass transport inside the drop. The effect of electric field is expressed in terms of L, the ratio of the maximum electric-field-induced surface velocity to translation-induced surface velocity. For a fixed value of L, compared to a steady uniform field, unsteady electric fields are more effective in enhancing heat transfer due to fluid mixing resulting from changing flow patterns. The enhancement in time periodic fields shows a non-monotonic dependence on electric field frequency. For low frequency, the time scale of electric field-induced mixing is large and hence transport enhancement is low. For very high frequency, the field changes before fluid particles have moved any significant distance which limits fluid mixing and the heat transport behavior remains essentially that of a purely translating drop. Therefore the optimum frequency that corresponds to the maximum transport enhancement lies between these two limits. Furthermore, with periodic fields for a fixed L, increase in Peclet number always increases the maximum heat transfer enhancement. However, for a fixed Peclet number, an increase in the electric field strength does not necessarily lead to an increase in heat transfer enhancement. Higher electric field strength leads to higher flow velocity (which facilitates heat transfer) but provides shorter time scale over which fluid mixing takes place (which is detrimental to heat transfer). These competing effects give rise to non-monotonic enhancement behavior with L. For unsteady non-uniform electric field, heat/mass transport is not enhanced when L < ∼0.5. For larger values of L, non-uniform electric field provides higher transport enhancement compared to the steady and unsteady uniform electric fields.